/* ----------------------------------------------------------------------  
* Copyright (C) 2010 ARM Limited. All rights reserved.  
*  
* $Date:        29. November 2010  
* $Revision: 	V1.0.3  
*  
* Project: 	    CMSIS DSP Library  
* Title:	    arm_lms_f32.c  
*  
* Description:	Processing function for the floating-point LMS filter.  
*  
* Target Processor: Cortex-M4/Cortex-M3
*  
* Version 1.0.3 2010/11/29 
*    Re-organized the CMSIS folders and updated documentation.  
*   
* Version 1.0.2 2010/11/11  
*    Documentation updated.   
*  
* Version 1.0.1 2010/10/05   
*    Production release and review comments incorporated.  
*  
* Version 1.0.0 2010/09/20   
*    Production release and review comments incorporated  
*  
* Version 0.0.7  2010/06/10   
*    Misra-C changes done  
* -------------------------------------------------------------------- */ 
 
#include "arm_math.h" 
 
/**  
 * @ingroup groupFilters  
 */ 
 
/**  
 * @defgroup LMS Least Mean Square (LMS) Filters  
 *  
 * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.  
 * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.  
 * Adaptive filters are often used in communication systems, equalizers, and noise removal.  
 * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.  
 * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.  
 *  
 * An LMS filter consists of two components as shown below.  
 * The first component is a standard transversal or FIR filter.  
 * The second component is a coefficient update mechanism.  
 * The LMS filter has two input signals.  
 * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.  
 * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.  
 * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.  
 * This "error signal" tends towards zero as the filter adapts.  
 * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.  
 * \image html LMS.gif "Internal structure of the Least Mean Square filter"  
 *  
 * The functions operate on blocks of data and each call to the function processes  
 * <code>blockSize</code> samples through the filter.  
 * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,  
 * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.  
 * All arrays contain <code>blockSize</code> values.  
 *  
 * The API functions operate on a block-by-block basis.  
 * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.  
 * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.  
 *  
 * \par Algorithm:  
 * The output signal <code>y[n]</code> is computed by a standard FIR filter:  
 * <pre>  
 *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]  
 * </pre>  
 *  
 * \par  
 * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:  
 * <pre>  
 *     e[n] = d[n] - y[n].  
 * </pre>  
 *  
 * \par  
 * After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:  
 * <pre>  
 *     b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1  
 * </pre>  
 * where <code>mu</code> is the step size and controls the rate of coefficient convergence.  
 *\par  
 * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.  
 * Coefficients are stored in time reversed order.  
 * \par  
 * <pre>  
 *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}  
 * </pre>  
 * \par  
 * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.  
 * Samples in the state buffer are stored in the order:  
 * \par  
 * <pre>  
 *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}  
 * </pre>  
 * \par  
 * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.  
 * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,  
 * to be avoided and yields a significant speed improvement.  
 * The state variables are updated after each block of data is processed.  
 * \par Instance Structure  
 * The coefficients and state variables for a filter are stored together in an instance data structure.  
 * A separate instance structure must be defined for each filter and  
 * coefficient and state arrays cannot be shared among instances.  
 * There are separate instance structure declarations for each of the 3 supported data types.  
 *  
 * \par Initialization Functions  
 * There is also an associated initialization function for each data type.  
 * The initialization function performs the following operations:  
 * - Sets the values of the internal structure fields.  
 * - Zeros out the values in the state buffer.  
 * \par  
 * Use of the initialization function is optional.  
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
 * To place an instance structure into a const data section, the instance structure must be manually initialized.  
 * Set the values in the state buffer to zeros before static initialization.  
 * The code below statically initializes each of the 3 different data type filter instance structures  
 * <pre>  
 *    arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};  
 *    arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};  
 *    arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};  
 * </pre>  
 * where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;  
 * <code>pCoeffs</code> is the address of the coefficient buffer; <code>mu</code> is the step size parameter; and <code>postShift</code> is the shift applied to coefficients.  
 *  
 * \par Fixed-Point Behavior:  
 * Care must be taken when using the Q15 and Q31 versions of the LMS filter.  
 * The following issues must be considered:  
 * - Scaling of coefficients  
 * - Overflow and saturation  
 *  
 * \par Scaling of Coefficients:  
 * Filter coefficients are represented as fractional values and  
 * coefficients are restricted to lie in the range <code>[-1 +1)</code>.  
 * The fixed-point functions have an additional scaling parameter <code>postShift</code>.  
 * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.  
 * This essentially scales the filter coefficients by <code>2^postShift</code> and  
 * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.  
 * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.  
 *  
 * \par Overflow and Saturation:  
 * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are  
 * described separately as part of the function specific documentation below.  
 */ 
 
/**  
 * @addtogroup LMS  
 * @{  
 */ 
 
  /**  
   * @brief Processing function for floating-point LMS filter.  
   * @param[in]  *S points to an instance of the floating-point LMS filter structure.  
   * @param[in]  *pSrc points to the block of input data.  
   * @param[in]  *pRef points to the block of reference data.  
   * @param[out] *pOut points to the block of output data.  
   * @param[out] *pErr points to the block of error data.  
   * @param[in]  blockSize number of samples to process.  
   * @return     none.  
   */ 
 
void arm_lms_f32( 
  const arm_lms_instance_f32 * S, 
  float32_t * pSrc, 
  float32_t * pRef, 
  float32_t * pOut, 
  float32_t * pErr, 
  uint32_t blockSize) 
{ 
  float32_t *pState = S->pState;                 /* State pointer */ 
  float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */ 
  float32_t *pStateCurnt;                        /* Points to the current sample of the state */ 
  float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */ 
  float32_t mu = S->mu;                          /* Adaptive factor */ 
  uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */ 
  uint32_t tapCnt, blkCnt;                       /* Loop counters */ 
  float32_t sum, e, d;                           /* accumulator, error, reference data sample */ 
  float32_t w = 0.0f;                            /* weight factor */ 
 
  e = 0.0f; 
  d = 0.0f; 
 
  /* S->pState points to state array which contains previous frame (numTaps - 1) samples */ 
  /* pStateCurnt points to the location where the new input data should be written */ 
  pStateCurnt = &(S->pState[(numTaps - 1u)]); 
 
  blkCnt = blockSize; 
 
  while(blkCnt > 0u) 
  { 
    /* Copy the new input sample into the state buffer */ 
    *pStateCurnt++ = *pSrc++; 
 
    /* Initialize pState pointer */ 
    px = pState; 
 
    /* Initialize coeff pointer */ 
    pb = (pCoeffs); 
 
    /* Set the accumulator to zero */ 
    sum = 0.0f; 
 
    /* Loop unrolling.  Process 4 taps at a time. */ 
    tapCnt = numTaps >> 2; 
 
    while(tapCnt > 0u) 
    { 
      /* Perform the multiply-accumulate */ 
      sum += (*px++) * (*pb++); 
      sum += (*px++) * (*pb++); 
      sum += (*px++) * (*pb++); 
      sum += (*px++) * (*pb++); 
 
      /* Decrement the loop counter */ 
      tapCnt--; 
    } 
 
    /* If the filter length is not a multiple of 4, compute the remaining filter taps */ 
    tapCnt = numTaps % 0x4u; 
 
    while(tapCnt > 0u) 
    { 
      /* Perform the multiply-accumulate */ 
      sum += (*px++) * (*pb++); 
 
      /* Decrement the loop counter */ 
      tapCnt--; 
    } 
 
    /* The result in the accumulator, store in the destination buffer. */ 
    *pOut++ = sum; 
 
    /* Compute and store error */ 
    d = (float32_t) (*pRef++); 
    e = d - sum; 
    *pErr++ = e; 
 
    /* Calculation of Weighting factor for the updating filter coefficients */ 
    w = e * mu; 
 
    /* Initialize pState pointer */ 
    px = pState; 
 
    /* Initialize coeff pointer */ 
    pb = (pCoeffs); 
 
    /* Loop unrolling.  Process 4 taps at a time. */ 
    tapCnt = numTaps >> 2; 
 
    /* Update filter coefficients */ 
    while(tapCnt > 0u) 
    { 
      /* Perform the multiply-accumulate */ 
      *pb = *pb + (w * (*px++)); 
      pb++; 
 
      *pb = *pb + (w * (*px++)); 
      pb++; 
 
      *pb = *pb + (w * (*px++)); 
      pb++; 
 
      *pb = *pb + (w * (*px++)); 
      pb++; 
 
      /* Decrement the loop counter */ 
      tapCnt--; 
    } 
 
    /* If the filter length is not a multiple of 4, compute the remaining filter taps */ 
    tapCnt = numTaps % 0x4u; 
 
    while(tapCnt > 0u) 
    { 
      /* Perform the multiply-accumulate */ 
      *pb = *pb + (w * (*px++)); 
      pb++; 
 
      /* Decrement the loop counter */ 
      tapCnt--; 
    } 
 
    /* Advance state pointer by 1 for the next sample */ 
    pState = pState + 1; 
 
    /* Decrement the loop counter */ 
    blkCnt--; 
  } 
 
 
  /* Processing is complete. Now copy the last numTaps - 1 samples to the  
     satrt of the state buffer. This prepares the state buffer for the  
     next function call. */ 
 
  /* Points to the start of the pState buffer */ 
  pStateCurnt = S->pState; 
 
  /* Loop unrolling for (numTaps - 1u) samples copy */ 
  tapCnt = (numTaps - 1u) >> 2u; 
 
  /* copy data */ 
  while(tapCnt > 0u) 
  { 
    *pStateCurnt++ = *pState++; 
    *pStateCurnt++ = *pState++; 
    *pStateCurnt++ = *pState++; 
    *pStateCurnt++ = *pState++; 
 
    /* Decrement the loop counter */ 
    tapCnt--; 
  } 
 
  /* Calculate remaining number of copies */ 
  tapCnt = (numTaps - 1u) % 0x4u; 
 
  /* Copy the remaining q31_t data */ 
  while(tapCnt > 0u) 
  { 
    *pStateCurnt++ = *pState++; 
 
    /* Decrement the loop counter */ 
    tapCnt--; 
  } 
} 
 
/**  
   * @} end of LMS group  
   */ 
